Question

If $f\left(x\right)=\{-x^2+2,x\le 0$
$x^2+\frac{15}{8},x>0$,
then

• A. $f\left(x\right)$ is increases at $x\ge 1$
• B. $x=0$ is a point of local maximum of $f\left(x\right)$
• C. $x=0$ is a point of discontinuity of $f\left(x\right)$
• D. $x=0$ is not an extrema of $f\left(x\right)$

Answer 1

Answer: (A), (C)

$x=0$ is a point of discontinuity of $f\left(x\right)$
$f\left(x\right)$ is increases at $x\ge 1$

By graph we can see that is is increasing function when $x>0.$

Also at $x=0,$ function $f\left(x\right)$ is discontinous.

but, we can not find maximum or minimum values at $x=0.$ Because at that point the graph is discontinous.